Abstract
Abstract. This paper presents a synthesis methodology of RCCC linkages based on the solution region methodology, R denoting a revolute joint and C denoting a cylindrical joint. The RCCC linkage is usually synthesized via its two defining dyads, RC and CC. For the four poses problem, there are double infinite solutions of the CC dyad, but there is no solution for the RC dyad. However, if a condition is imposed that leads to a coupling of the two dyads, a maximum of four poses can be visited with the RCCC linkage. Unfortunately, until now, there is no methodology to synthesize the RCCC linkage for four given poses besides optimization method. According to the coupling condition above, infinite exact solutions of RCCC linkages can be obtained. For displaying these RCCC linkages, we first build a spherical 4R linkage solution region. Then solutions with circuit and branch defects can be eliminated on this solution region, so that the feasible solution region is obtained. An RCCC linkage can be obtained by using the prescribed spatial positions and selected a value on the feasible solution region. We take values on the feasible solution region by a certain step length and many exact solutions for RCCC linkages can be obtained. Finally we display these solutions on a map, this map is the solution region for RCCC linkages.
Highlights
The synthesis of spatial RCCC linkages has been received much more attentions recently
In some literatures (Bai and Angeles, 2015), RC dyad is synthesized by optimization method and CC dyad is synthesized by line congruence, only one approximate solution for RCCC linkage can be obtained for four poses
We proposed the primary idea of the synthesis of RCCC linkages for four poses by solution region map (Cao and Han, 2016; Han and Cao, 2017), but the method of building solution region isn’t given
Summary
The synthesis of spatial RCCC linkages has been received much more attentions recently. A semi-graphical approach is proposed for the synthesis of 4C linkage for five given poses to obtain a robust solution (Bai and Angeles, 2012). In some literatures (Bai and Angeles, 2015), RC dyad is synthesized by optimization method and CC dyad is synthesized by line congruence, only one approximate solution for RCCC linkage can be obtained for four poses. For synthesizing more RCCC linkages, we propose a solution region methodology by which infinite exact solutions can be obtained. We proposed the primary idea of the synthesis of RCCC linkages for four poses by solution region map (Cao and Han, 2016; Han and Cao, 2017), but the method of building solution region isn’t given
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